"This is our land," Arseniy Yatsenyuk told a crowd gathered at the Kiev statue to writer and nationalist Taras Shevchenko.
"Our fathers and grandfathers have spilled their blood for this land. And we won't budge a single centimetre from Ukrainian land. Let Russia and its president know this."
"We are one country, one family and we're here together with our kobzar (bard) Taras," said acting President Oleksandr Turchynov.
Later today, following an extraordinary meeting of the Ukrainian government, Yatsenyuk announced he would be flying this week to the United States for high-level talks on "resolution of the situation in Ukraine," the Interfax news agency reported.
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Crimea, a strategic peninsula in southern Ukraine, has become the flashpoint in the battle for Ukraine, where three months of protests sparked by President Victor Yanukovych's decision to ditch a significant treaty with the 28-nation European Union after strong pressure from Russia led to his downfall.
This weekend, Russia reinforced its armed presence on the peninsula. Russian President Vladimir Putin's foreign minister ruled out any dialogue with Ukraine's new authorities, whom he dismissed as the puppets of extremists.
The regional parliament in Crimea has set a March 16 referendum on leaving Ukraine to join Russia. Senior lawmakers in Moscow have said they would support the move, ignoring sanctions threats and warnings from President Barack Obama that the vote would violate international law.